Bell Work

If the radius of a circle is 13 cm, then what is the circumference?

If two angles of a triangle are 45 degrees, then what is the 3rd angle measurement?

Answer:

2π(13cm) = 2(3.14)(13cm) = 81.64cm

90°

Lesson 4: Review of Arithmetic

Number*: An idea

Numeral*: A symbol that we use to express the idea of a particular number.

The value of a numeral is the number represented by the numeral.

Easier way to understand this:You are a person, and there is just one of you. But different people call you by different names. Your name isn’t you, it just represents you.It’s the same thing with number and numeral. A number is an idea but a numeral is what is used to represent that idea. For example, there could be three pencils on my desk. I know there are three objects, however a way I could put this down on paper to represent it would be to say there are “3” pencils.

Counting Numbers (or Natural Numbers): When we begin counting, we always begin with the number 1 and follow it with the number 2 etc. Thus counting numbers are (1, 2, 3, 4, ……).

Real Numbers: A value that represents a quantity or a distance on a number line. This includes all rational (-5, ⅔) and all irrational (√2, π).

Number Line: The number line can be used as a graphic aid when discussing positive and negative numbers.

To graph a point on the number, we place a closed dot on that corresponding number.

Graph the following points on a number line.

-5, 1, -2, 3.5, -2.5, 2.5

Answer: -5, -2.5, -2, 1, 2.5, 3.5

Multiplication of Fractions:Fractions are multiplied by multiplying the numerators to get the new numerator, and by multiplying the denominators to get the new denominator.

Example:

4/3 x 7/5

5/7 x 2/3

Answer:

4/3 x 7/5 = 4x7/3x5 = 28/15 = 1 13/15

5/7 x 2/3 = 5x2/7x3 = 10/21

Diving Fractions:We divide fractions by inverting the divisor and then multiplying.

Example:

4/3 ÷ 15/8

5/6 ÷ 3/4

Answer:

4/3 ÷ 15/8 = 4/3 x 8/15 = 4x8/3x15 = 32/45

5/6 ÷ 3/4 = 5/6 x 4/3 = 5x4/6x3 = 20/18 = 1 2/18 = 1 1/9

If cancellation is possible, it is easier if we cancel before we multiply.Example: solve by cancelling

7/3 x 30/9

3/5 x 5/6 x 21/23

Answer:

7/3 x 30/9 = 7/1 x 10/9 = 70/9 = 7 7/9

3/5 x 5/6 x 21/23 = 1/1 x ½ x 21/23 = 21/46

Change mixed numbers to improper fractions and then multiply or divide as indicated.Example:

2 ½ x 5 ⅓

12 ⅓ ÷ 2 ⅙

Answer:

2 ½ x 5 ⅓ = 5/2 x 16/3 = 5/1 x 8/3 = 40/3 = 13 ⅓

12 ⅓ ÷ 2 ⅙ = 37/3 x 6/13 = 37/1 x 2/13 = 74/13 = 5 9/13

We use the equals sign to designate two quantities are equal.

5 + 2 = 7In the same way we use the ≠ symbol to designate that two quantities are not equal.

5 + 2 ≠ 11

Basic Operations: Addition = SumSubtraction = DifferenceMultiplication = ProductDivision = Quotient

Operations with decimal numbers:We must align the decimal points vertically when we add and subtract decimal numbers.Example:

1.005 + 300.012

4.0016 – 0.02163

Answer:

1.005 + 300.012 = 301.017

4.0016 – 0.02163 = 3.97997

We do not alight the decimal points when we multiply.Example:

4.06 x 0.016

Answer:

4.06 x 0.016 = 0.06496

When we divide, we adjust the decimal points as necessary.Example:

6.039 ÷ 0.03

Answer:

6.039 ÷ 0.03 = 603.9 ÷ 3 = 201.3

Unit Multiplier: 3 ft/1yd and 1yd/3ft are both equal to 1. We call these fractions unit multipliers. We can use unit multipliers to change the units of a number.

Example: Use one unit multiplier to convert 32 feet to inches. (1ft = 12 inches)

Answer: = 32 ft / 1 x 12 inches / 1 ftFeet cancel out= 32 x 12 inches / 1= 384 inches

Example: Use one unit multiplier to convert 36 feet to miles. (5280 feet = 1 mile)

Answer:= 36 feet / 1 x 1 mile / 5280 feetFeet cancel out= 36 miles / 5280≈0.0068 miles

Equivalent Measures:1 foot = 12 inches1 meter = 100 cm1 yard = 3 feet1 cm = 10 mm1 inch = 2.54 cm1 mile = 5280 feet1 km = 1000 m

Practice: Solve the following without a calculator

4 ½ x 2 ⅘

3 ¼ ÷ 1 ⅜

Answer:

4 ½ x 2 ⅘ = 9/2 x 14/5 = 63/5 = 12 ⅗

3 ¼ ÷ 1 ⅜ = 13/4 ÷ 11/8 = 13/4 x 8/11 = 26/11 = 2 4/11

HW: Lesson 4 #1-30